When designing optical systems, such as cameras, sensors, optical instruments, electro-optical devices, etc., designers use computational modeling to test the performance of the designs. By modeling the scene image output of optical systems, designers can predict errors before the optical system is made or deployed. Therefore, these errors can be corrected before the optical system is actually built. Thus, modeling the scene image output saves both time and resources that could have been wasted by building a design that does not meet the desired specification.
FIG. 1 illustrates a typical optical system 1. As light rays 30 from an object scene pass through a lens 10, they intercept an image plane 40, thereby forming an image on the plane 40. In FIG. 1, the image plane 40 happens to be located on an image sensor 20, so the image formed on the image plane 40 corresponds to the image received at image sensor 20.
FIG. 2a illustrates an image 50 formed at the image plane 40 of the optical system 1 (FIG. 1). In order to model this image, designers view the image as having many points, such as point P. Through computation, designers are able to determine the image characteristics of the image 50 at the various points P throughout the image 50. Image characteristics might vary depending on qualities associated with the lens 10, such as the lens prescription.
Designers are able to specify the location of points P in the image using a polar coordinate system, such as that illustrated in FIG. 2b. Specifically, in a polar coordinate system, each point can be described by a radial distance r and an angle θ. Distance rp represents the length between the origin O of the polar coordinate system and the selected point P in the image 50. For example, FIG. 2b shows a point P that is rp length units away from the origin O. The length rp may be represented using nanometers or any other unit of length. Angle θ represents the angle between the selected point P and the polar axis x. For example, point P in FIG. 2b is θp angular units away from the polar axis (e.g., 0°). The angle θ may be represented using degrees, radians, or any other unit for describing an angle.
In addition to modeling characteristics at a point P in the image 50 according to the point's physical location (rp, θp), designers may also model characteristics specific to different wavelengths of light at point P. Thus, wavelength λp is also associated with point P.
One particular image characteristic that designers would like to have information about before building an optical system is the impulse response at various points and wavelengths in a simulated image. This impulse response is also known as the point spread function. The point spread function of an optical system is a widely used characteristic that describes the response of the optical system to a point source or a point object and also describes the amount of blur introduced into a recorded image. Traditionally, optical ray tracing programs, such as ZEMAX®, available from ZEMAX® Development Corp., 3001 112th Ave. NE, Bellevue, Wash. 98004, have been used to compute this data for each point in the image. However, modeling using ray tracing to determine the point spread function for each point in the image is impractical because of its high computational demands, especially as image sizes and resolutions have increased. Known methods also result in undesirable image artifacts in the simulated image.
Accordingly, there exists a need in the art for improved techniques for determining the point spread function at points in a simulated image from an optical system.